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Question

Esther, Beowulf, Cwene, and Durwyn were dividing up a bag of gold coins from a dragon's hoard

 

Esther took three more than one quarter of the coins in the bag 

Beowulf took two more than one third of the coins remaining in the bag 

Cwene took four more than one half of the coins remaining in the bag 

This left eighteen coins for Durwyn 

 

How many coins were in the bag? 

Answer 1

Hi, Stephanie -

 

Let T = total number of coins in the bag.

 

1)  Esther took 3 more than 1/4 of the coins.   Write this as E = 3 + T/4.    

 

What's left in the bag?  T - (3 + T/4) = T - 3 - T/4 = (3T)/4 - 3   

 

2)  Beowulf took 2 more than one third of what's left.    Write this as B = 2 + [(3T/4 - 3)]/3

 

So 3T/4 divided by 3 is T/4.  -3/3 = -1   so B = 2 + T/4 - 1 = 1 + T/4

 

What's left in the bag?  (3T/4 - 3) - (1 + T/4) = 3T/4 - T/4 - 3 - 1 = 2T/4 -4 = T/2 - 4

 

3)  So now Cwene takes 4 more than 1/2 of what's left.   C = 4 + (T/2 - 4)/2 = 4 + T/4 - 2 = 2 + T/4

 

What's left in the bag?  (T/2 - 4) - (2 + T/4) = T/2 - T/4 - 4 - 2 = T/4 - 6

 

4)  Durwyn gets the remaining 18 coins.  

So 18 = T/4 - 6  (What's left after Cwene takes his share.)

 

Solve for T:  24 = T/4    T = 96

 

5)  Do these amounts add up to 96?  

 

Esther:  T/4 + 3 = 96/4 + 3 = 24 + 3 = 27

Beowulf:  T/4 + 1 = 96/4 + 1 = 24 + 1 = 25

Cwene:  T/4 + 2 = 96/4 + 2 = 24 + 2 = 26

Durwyn:  18

 

27 + 25 + 26 + 18 = 96

 

Let me know if you have any questions.

 

Ms. Horvath